A necessary and sufficient condition for positive solutions for fourth-order multi-point boundary value problems with p-Laplacian

In this paper, we consider the existence of positive solutions for a class of singular fourth-order p-Laplacian equation with multi-point boundary conditions. By means of a monotone iterative technique, a necessary and sufficient condition for the existence of a pseudo-C3[0,1] positive solution is established. Also, the existence and uniqueness of the pseudo-C3[0,1] positive solution, the iterative sequence of the solution and an error estimation for the pseudo-C3[0,1] positive solution are obtained.